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Sections 4.3 (The master method) and 4.4 (Proof of the master theorem), pp. 73–90. Michael T. Goodrich and Roberto Tamassia. Algorithm Design: Foundation, Analysis, and Internet Examples. Wiley, 2002. ISBN 0-471-38365-1. The master theorem (including the version of Case 2 included here, which is stronger than the one from CLRS) is on pp. 268 ...
In computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorithms where the sub-problems have substantially different sizes.
In mathematics, a theorem that covers a variety of cases is sometimes called a master theorem. Some theorems called master theorems in their fields include: Master theorem (analysis of algorithms), analyzing the asymptotic behavior of divide-and-conquer algorithms; Ramanujan's master theorem, providing an analytic expression for the Mellin ...
In mathematics, Ramanujan's master theorem, named after Srinivasa Ramanujan, [1] is a technique that provides an analytic expression for the Mellin transform of an analytic function. Page from Ramanujan's notebook stating his Master theorem.
D. Foata and G.-N. Han, A new proof of the Garoufalidis-Lê-Zeilberger Quantum MacMahon Master Theorem, Journal of Algebra 307 (2007), no. 1, 424–431 . D. Foata and G.-N. Han, Specializations and extensions of the quantum MacMahon Master Theorem, Linear Algebra and its Applications 423 (2007), no. 2–3, 445–455 .
Gaspar da Cruz (c. 1520 – 5 February 1570; sometimes also known under an Hispanized version of his name, Gaspar de la Cruz [1]) was a Portuguese Dominican friar born in Évora, who traveled to Asia and wrote one of the first detailed European accounts about China.
Lamé's Theorem is the result of Gabriel Lamé's analysis of the complexity of the Euclidean algorithm. Using Fibonacci numbers , he proved in 1844 [ 1 ] [ 2 ] that when looking for the greatest common divisor (GCD) of two integers a and b , the algorithm finishes in at most 5 k steps, where k is the number of digits (decimal) of b .
The theorem is a foregone conclusion over classical logic, where law of the excluded middle is assumed. The proof below is therefore given using the means of a constructive set theory . It is evident from the proof how the theorem relies on the axiom of pairing as well as an axiom of separation , of which there are notable variations.